See picture. If this were anywhere else id be able to fix it easily. i have an idea to just color code the 2 wires, cut out the fat part, and reconnect the 2 wires. however I do not know if the fat part serves some critical purpose, or if there is an easier fix.

 

The "fat part" is just a strain relief. You can cut it out and connect the wires directly.

 

Agreed, although I think you could pull the fresh wire through the strain relief to reuse it. It doesn't seem to work real well but it's probably better than nothing.

 

I had a hair trimmer (back when I had hair) that ended up with the same problem. Two things I did was to remove the strain relief and run the wires to the switches just as before. Where the wires exited the trimmer I Hot Melt Glued the wire so it wouldn't pull on the inner connections AND support the wire where it exited the trimmer. Support is important to prevent just the sort of thing you have found. Fatigue of bending repeatedly at a given point can break the insulation and can even break the wire inside the insulation. But yes, it's an easy fix. Just make sure that the inner connections are not in danger of being pulled out accidentally. Support the wire.

I think you could pull the fresh wire through the strain relief to reuse it.

I've seen that done too. Not always easy and sometimes it can end up being less than supporting. But worth a try.

 

Considering that what we see is a mains voltage connection, attention to details is important.
What I think that I see is that the cord passes thru that molded on strain relief and is terminated soldered into a printed circuit board.
What I would do is to unsolder the wires from the circuit board, and then cut off the cord at the bare spot. Then I would split open that molded strain relief section, remove the fragment of cord, and adhere it to the cord. Then I would again solder the two wires back into the circuit board.
It might also work well to simply remove the wires from the PCB, curt off the damaged section, and reattach them directly to the PCB by soldering them again.


BUT if you are not good at soldering, there is also a plastic repair material that can be applied to that failed section of insulation to seal the connection back up.